For discrete multiple orthogonal polynomials such as the multiple Charlier polynomials, the multiple Meixner polynomials, and the multiple Hahn polynomials, we first find a lowering operator and then give a (r + 1)th order difference equation by combining the lowering operator with the raising operator. As a corollary, explicit third order difference equations for discrete multiple orthogonal p...

Certain properties of optimal bitwise APP (A Posteriori Probability) decoding of binary linear block codes are studied. The focus is on the Probability Density Function (pdf) of the bit Log-Likelihood-Ratio (LLR). A general channel model with discrete (not necessarily binary) input and discrete or continuous output is considered. It is proved that under a set of mild conditions on the channel, ...

Article history: Received 18 July 2013 Received in revised form 9 May 2014 Accepted 15 May 2014 Available online 22 May 2014 Highly volatile scenarios, such as those provoked by the recent subprime and sovereign debt crises, have questioned the accuracy of current risk forecasting methods. This paper adds fuel to this debate by comparing the performance of alternative specifications for modelin...

We describe various aspects of the Al-Salam-Carlitz q-Charlier polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.

We describe various aspects of the Al-Salam-Chihara q-Charlier polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial proof of Anshelevich’s recent result on the linearization coefficients.

In this paper, we consider Poisson-Charlier and poly-Cauchy mixed type polynomials and give various identities of those polynomials which are derived from umbral calculus. 424 Dae San Kim, Dmitry V. Dolgy, Taekyun Kim and Jong-Jin Seo